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Projective Method
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting n as the number of variables and L as the number of bits of input to the algorithm, Karmarkar's algorithm requires O(n^ L) operations on O(L) digit numbers, as compared to O(n^6 L) such operations for the ellipsoid algorithm. The runtime of Karmarkar's algorithm is thus :O(n^ L^2 \cdot \log L \cdot \log \log L) using FFT-based multiplication (see Big O notation). Karmarkar's algorithm falls within the class of interior point methods: the current guess for the solution does not follow the boundary of the feasible set as in the simplex method, but it moves through the interior of the feasible region, improving the approximation of the optimal solution by a definite fraction wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considered among the most prestigious universities in the world. Stanford was founded in 1885 by Leland and Jane Stanford in memory of their only child, Leland Stanford Jr., who had died of typhoid fever at age 15 the previous year. Leland Stanford was a U.S. senator and former governor of California who made his fortune as a railroad tycoon. The school admitted its first students on October 1, 1891, as a coeducational and non-denominational institution. Stanford University struggled financially after the death of Leland Stanford in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, provost of Stanford Frederick Terman inspired and supported faculty and graduates' entrepreneu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Processor
In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called ''vectors''. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SWAR Arithmetic Units. Vector processors can greatly improve performance on certain workloads, notably numerical simulation and similar tasks. Vector processing techniques also operate in video-game console hardware and in graphics accelerators. Vector machines appeared in the early 1970s and dominated supercomputer design through the 1970s into the 1990s, notably the various Cray platforms. The rapid fall in the price-to-performance ratio of conventional microprocessor designs led to a decline in vector superc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barrier Function
In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value on a point increases to infinity as the point approaches the boundary of the feasible region of an optimization problem. Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to handle. The two most common types of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated by their connection with primal-dual interior point methods. Motivation Consider the following constrained optimization problem: :minimize :subject to where is some constant. If one wishes to remove the inequality constraint, the problem can be re-formulated as :minimize , :where if , and zero otherwise. This problem is equivalent to the first. It gets rid of the inequality, but introduces the issue that the penalty function , and there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projected Newton Barrier Method
Projected is an American rock supergroup consisting of Sevendust members John Connolly and Vinnie Hornsby, Alter Bridge and Creed drummer Scott Phillips, and former Submersed and current Tremonti guitarist Eric Friedman. The band released their album, ''Human'', in June 2012, before falling into inactivity as members returned to their respective bands in late 2012. The band released their second studio album, the double album, ''Ignite My Insanity'', in July 2017. They reconvened in early 2020 and finished recording their third album in July 2020. History The band recorded as a four-piece, with each of the members coming from different bands. John Connolly and Vinnie Hornsby had both played together for many years in the alternative metal band Sevendust, as the guitarist and bassist respectively. Eric Friedman had previously been the guitarist for the now-defunct band Submersed, currently playing with Tremonti (formed with Mark Tremonti, Garrett Whitlock, Wolfgang Van ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Gill
Philip, also Phillip, is a male given name, derived from the Greek (''Philippos'', lit. "horse-loving" or "fond of horses"), from a compound of (''philos'', "dear", "loved", "loving") and (''hippos'', "horse"). Prominent Philips who popularized the name include kings of Macedonia and one of the apostles of early Christianity. ''Philip'' has many alternative spellings. One derivation often used as a surname is Phillips. It was also found during ancient Greek times with two Ps as Philippides and Philippos. It has many diminutive (or even hypocoristic) forms including Phil, Philly, Lip, Pip, Pep or Peps. There are also feminine forms such as Philippine and Philippa. Antiquity Kings of Macedon * Philip I of Macedon * Philip II of Macedon, father of Alexander the Great * Philip III of Macedon, half-brother of Alexander the Great * Philip IV of Macedon * Philip V of Macedon New Testament * Philip the Apostle * Philip the Evangelist Others * Philippus of Croton (c. 6th cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Art
Prior art (also known as state of the art or background art) is a concept in patent law used to determine the patentability of an invention, in particular whether an invention meets the novelty and the inventive step or non-obviousness criteria for patentability. In most systems of patent law, prior art is generally defined as anything that is made available, or disclosed, to the public that might be relevant to a patent's claim before the effective filing date of a patent application for an invention. However, notable differences exist in how prior art is specifically defined under different national, regional, and international patent systems. The prior art is evaluated by patent offices as part of the patent granting process in what is called “substantive examination” of a patent application in order to determine whether an invention claimed in the patent application meets the novelty and inventive step or non-obviousness criteria for patentability. It may also be cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA (algorithm)
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ) (the British signals intelligence agency) by the English mathematician Clifford Cocks. That system was declassified in 1997. In a public-key cryptosystem, the encryption key is public and distinct from the decryption key, which is kept secret (private). An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers. The security of RSA relies on the practical difficulty of factoring the produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ronald Rivest
Ronald Linn Rivest (; born May 6, 1947) is a cryptographer and an Institute Professor at MIT. He is a member of MIT's Department of Electrical Engineering and Computer Science (EECS) and a member of MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL). His work has spanned the fields of algorithms and combinatorics, cryptography, machine learning, and election integrity. Rivest is one of the inventors of the RSA algorithm (along with Adi Shamir and Len Adleman). He is the inventor of the symmetric key encryption algorithms RC2, RC4, RC5, and co-inventor of RC6. The "RC" stands for "Rivest Cipher", or alternatively, "Ron's Code". (RC3 was broken at RSA Security during development; similarly, RC1 was never published.) He also authored the MD2, MD4, MD5 and MD6 cryptographic hash functions. Education Rivest earned a Bachelor's degree in Mathematics from Yale University in 1969, and a Ph.D. degree in Computer Science from Stanford University in 197 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New York Times
''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid digital subscribers. It also is a producer of popular podcasts such as '' The Daily''. Founded in 1851 by Henry Jarvis Raymond and George Jones, it was initially published by Raymond, Jones & Company. The ''Times'' has won 132 Pulitzer Prizes, the most of any newspaper, and has long been regarded as a national " newspaper of record". For print it is ranked 18th in the world by circulation and 3rd in the U.S. The paper is owned by the New York Times Company, which is publicly traded. It has been governed by the Sulzberger family since 1896, through a dual-class share structure after its shares became publicly traded. A. G. Sulzberger, the paper's publisher and the company's chairman, is the fifth generation of the family to head the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Patent
A software patent is a patent on a piece of software, such as a computer program, libraries, user interface, or algorithm. Background A patent is a set of exclusionary rights granted by a state to a patent holder for a limited period of time, usually 20 years. These rights are granted to patent applicants in exchange for their disclosure of the inventions. Once a patent is granted in a given country, no person may make, use, sell or import/export the claimed invention in that country without the permission of the patent holder. Permission, where granted, is typically in the form of a license which conditions are set by the patent owner: it may be free or in return for a royalty payment or lump sum fee. Patents are territorial in nature. To obtain a patent, inventors must file patent applications in each and every country in which they want a patent. For example, separate applications must be filed in Japan, China, the United States and India if the applicant wishes to obtai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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